While highly dense digital circuits (e.g., VLSI memories and microprocessors with hundreds of millions of devices on a single chip) are commonplace, designers have been much less successful condensing analog circuits into smaller and smaller areas. One reason this has been difficult is that analog circuits typically require a number of passive elements that are not easily shrunk. Resistors are necessary, for example, to bias operational amplifiers (op-amps) and play an important role in analog circuits. A typical analog to digital (A/D) converter or digital to analog (D/A) converter may use what is known as a resistor ladder to generate reference voltages for a group of parallel op-amps converting from one domain to the other.
A typical resistor may be formed in an integrated circuit (IC) from a (relatively) long run of a narrow strip of non-metal conductive material, e.g., polysilicon or doped silicon junction. Unfortunately, these long runs also have a relatively high capacitance per unit length, thus acting as a distributed RC with the R and C being the resistance and capacitance per unit length, respectively. Consequently, application of a voltage at one end may not be exhibited at the other until some time later because of the inherent delay in the distributed RC. Also, the larger the resistor, the longer the run and the more likely the capacitance is affected by other on chip activity, e.g., wiring on an adjacent layer, wiring that runs parallel but on the same layer, and etc. Moreover, these sources of additional capacitance are also noise sources that can disturb a sensitive measurement at the worst possible time, but are impossible to identify and isolate.
While relatively small (area) resistors with low resistance may be made without suffering from appreciable variation from resistor to resistor, shrinking larger resistor runs needed for higher resistance does not provide such typically consistent results. The long, narrow, thin lines used for these higher-resistance resistors are much more sensitive to line width variations because, to minimize resistor size, they are made at minimum line widths to maximize resistance per unit length. Since process variations may cause minimum width lines to vary as much as 2×, this can cause the resistance to vary as much as 2× also.
Although occasionally, fused lines have been used to trim resistance to desired values, generally, designers have found off chip resistor packs a simpler solution. Unfortunately, both of these approaches expand chip size. Fuses need a window through upper chip layers and clearance to adjacent features to avoid damaging other circuits; off chip resistors require wiring, pads and etc. to connect to on-chip circuits. Consequently, resistors are seldom integrated with analog circuits and analog circuits are seldom integrated with digital circuits. So, unfortunately, analog chips are typically larger than much denser digital chips.
Thus, there is a need to reduce resistor size for on-chip resistors and to provide a broad range of resistances for such on-chip resistors.